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This research introduces a novel Boltzmann Generator framework specifically designed to handle the complex symmetries of amorphous materials, addressing a critical gap where existing continuous-flow models fail. While equivariant graph neural networks improve sampling accuracy, the study uncovers an intrinsic limitation in current formulations: accumulated numerical errors break time-reversibility and compromise exact thermodynamic reweighting. These findings highlight fundamental challenges for generative AI applied to statistical mechanics and suggest that future architectures must prioritize preserving strict physical consistency over pure flow efficiency.
Boltzmann generators for amorphous particle systems
arXiv:2512.16607v2 Announce Type: replace-cross Abstract: Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann Generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann Generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann Generators, but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.
Abstract:Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann Generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann Generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann Generators, but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.
30 pages, 10 figures. V2 considerably expands the results compared to v1
Machine Learning (stat.ML); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
arXiv:2512.16607 [stat.ML]
(or arXiv:2512.16607v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2512.16607 Focus to learn more arXiv-issued DOI via DataCite
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